RBSE Class 12 Maths Solutions Chapter 2 Inverse Trigonometric Functions Ex 2.1

RBSE Class 12 Maths Solutions Chapter 2 Inverse Trigonometric Functions Ex 2.1

Question 1.

Find the principal value of sin-1 $(-\frac{1}{2})$.
Answer:

Question 2.
Find the principal value of cos-1 $\left(\frac{\sqrt{3}}{2}\right)$.
Answer:

Question 3.
Find the principal value of cosec-1 (2).
Answer:
Let cosec-1 (2) = y ⇒ cosec y = 2
We know that range of principal branch of cosec-1 is $[-\frac{\pi }{2},\frac{\pi }{2}]$ - {0}
And cosec $\left(\frac{\pi }{6}\right)$ = 2, where $\frac{\pi }{6}\in [-\frac{\pi }{2},\frac{\pi }{2}]-\left\{0\right\}$
Thus, principal value of cosec-1 (2) is $\frac{\pi }{6}$.

Question 4.
Find the principal value of tan-1 (- √3).
Answer:

Question 5.
Find the principal value of cos-1 $(-\frac{1}{2})$.
Answer:

Question 6.
Find the principal value of tan-1 (- 1).
Answer:
Let tan-1 (- 1) = y ⇒ tan y = - 1
We know that range of principal branch of tan-1 is $(-\frac{\pi }{2},\frac{\pi }{2})$.

Question 7.
Find the principal value of sec-1 $\left(\frac{2}{\sqrt{3}}\right)$.
Answer:

Question 8.
Find the principal value of cot-1 (√3).
Answer:
Let cot-1 (√3) = y
∴ cot y = √3
We know that range of principal branch of cot-1 is (0, π).
And cot $\left(\frac{\pi }{6}\right)$ = √3, where $\frac{\pi }{6}$ ∈ (0, π)
Thus, principal value of cot-1 (√3) is $\frac{\pi }{6}$.

Question 9.
Find the principal value of cos-1$(-\frac{1}{\sqrt{2}})$.
Answer:

Question 10.
Find the principal value of:
cosec-1 (- √2).
Answer:

Question 11.
Find the value of tan-1 (1) + cos-1 $(-\frac{1}{2})$ + sin-1$(-\frac{1}{2})$
Answer:

Question 12.
Find the value of:
cos-1$\left(\frac{1}{2}\right)$ + 2 sin-1$\left(\frac{1}{2}\right)$
Answer:
Range of cos-1 and sin-1 are (0, π) and (- π/2, π/2) respectively.

Question 13.
If sin-1 x = y, then:
(A) 0 ≤ y ≤ π
(B) - $\frac{\pi }{2}$ ≤ y ≤ $\frac{\pi }{2}$
(C) 0 < y < π
(D) - $\frac{\pi }{2}$ < y < $\frac{\pi }{2}$
Answer:

Question 14.
tan-1 √3 - sec-1 (- 2) is equal to:
(A) π
(B) - $\frac{\pi }{3}$
(C) $\frac{\pi }{3}$
(D) $\frac{2\pi }{3}$
Answer:

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